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Simplifying -150 = -16x2 + 128x + 6 Reorder the terms: -150 = 6 + 128x + -16x2 Solving -150 = 6 + 128x + -16x2 Solving for variable 'x'. Combine like terms: -150 + -6 = -156 -156 + -128x + 16x2 = 6 + 128x + -16x2 + -6 + -128x + 16x2 Reorder the terms: -156 + -128x + 16x2 = 6 + -6 + 128x + -128x + -16x2 + 16x2 Combine like terms: 6 + -6 = 0 -156 + -128x + 16x2 = 0 + 128x + -128x + -16x2 + 16x2 -156 + -128x + 16x2 = 128x + -128x + -16x2 + 16x2 Combine like terms: 128x + -128x = 0 -156 + -128x + 16x2 = 0 + -16x2 + 16x2 -156 + -128x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -156 + -128x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-39 + -32x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-39 + -32x + 4x2)' equal to zero and attempt to solve: Simplifying -39 + -32x + 4x2 = 0 Solving -39 + -32x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9.75 + -8x + x2 = 0 Move the constant term to the right: Add '9.75' to each side of the equation. -9.75 + -8x + 9.75 + x2 = 0 + 9.75 Reorder the terms: -9.75 + 9.75 + -8x + x2 = 0 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + -8x + x2 = 0 + 9.75 -8x + x2 = 0 + 9.75 Combine like terms: 0 + 9.75 = 9.75 -8x + x2 = 9.75 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 9.75 + 16 Reorder the terms: 16 + -8x + x2 = 9.75 + 16 Combine like terms: 9.75 + 16 = 25.75 16 + -8x + x2 = 25.75 Factor a perfect square on the left side: (x + -4)(x + -4) = 25.75 Calculate the square root of the right side: 5.074445783 Break this problem into two subproblems by setting (x + -4) equal to 5.074445783 and -5.074445783.Subproblem 1
x + -4 = 5.074445783 Simplifying x + -4 = 5.074445783 Reorder the terms: -4 + x = 5.074445783 Solving -4 + x = 5.074445783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.074445783 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.074445783 + 4 x = 5.074445783 + 4 Combine like terms: 5.074445783 + 4 = 9.074445783 x = 9.074445783 Simplifying x = 9.074445783Subproblem 2
x + -4 = -5.074445783 Simplifying x + -4 = -5.074445783 Reorder the terms: -4 + x = -5.074445783 Solving -4 + x = -5.074445783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.074445783 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.074445783 + 4 x = -5.074445783 + 4 Combine like terms: -5.074445783 + 4 = -1.074445783 x = -1.074445783 Simplifying x = -1.074445783Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.074445783, -1.074445783}Solution
x = {9.074445783, -1.074445783}
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